An interest in the local history and antiquities of her adopted county of Shropshire led her to folklore, but the defining moment came when her notes were shown to Miss Georgina Jackson in the early 1870s. Jackson had for many years been working on a projected book on Shropshire dialect, and had collected much folklore in the process, but failing health prompted her to hand the projects to Burne for completion. The latter thus brought out the planned Shropshire Word-Book (1879) and, after adding a great deal of her own material, Shropshire Folk-Lore (1883), which proved to be one of the best of the regional folklore collections and is still in demand today. Burne also joined the Folklore Society in 1883, and was soon involved on its Council and in various organizing roles, editing the journal Folk-Lore (1899–1908) and serving two terms as the Society's President (1909–10). In her first presidential address (Folk-Lore 21 (1910) she claimed, probably correctly, to be the first female president of a learned society in Britain. She continued to contribute numerous articles and notes to folklore journals and to local Shropshire/Staffordshire periodicals for the rest of her life, and her other major publication was the second edition of the influential Handbook of Folk-Lore (1914), for the Folklore Society.
Burne's particular forte was fieldwork, in contrast to her fellow folklorists who were primarily library scholars and thinkers, basing their theories on other people's books and manuscripts. Shropshire Folk-Lore demonstrated the wealth of material waiting to be collected, and also identified an important practical role available to those interested in the subject but unable to indulge in high theory. She became an advocate of fieldwork, urging systematic collecting programmes, offering advice on how to go about it, and urging high standards of documentation. In the process, she experimented with methods such as the geographical mapping of calendar custom variants, which were later to be adopted as normal practice. At the time of her death, she was working, with the Society's ‘Brand Committee’, on an ambitious plan to publish a new comprehensive survey of customs, to serve as an updated and expanded edition of Brand's Observations on Popular Antiquities.
Burne's major articles were ‘The Collection of English Folk-Lore’, Folk-Lore 1 (1890), 313–30; ‘The Value of European Folklore in the History of Culture’, Folk-Lore 21 (1910), 14–41; ‘The Scientific Aspects of Folklore’, Folk-Lore 22 (1911), 14–32.
Obituary: Folk-Lore 34 (1923), between pp. 99 and 100;Dorson, 1968: 318–22;Gordon Ashman, Talking Folklore 1:1 (1986), 6–21 and in Davidson and Blacker, 2001: 33–44;Simon J. Bronner, Folklore Women's Communication 24 (1981), 14–19.